financial mathematics its introduction and norms
- 2. INDEX 1.What is Capital Budgeting? 2.Process of CB 3.Components of CB 4.Non-Discounting Techniques a)Payback Period b)Average Rate of Return 5.Discounting Techniques a)Net Present Value b)Internal Rate Of Return c)Profitability Index
- 3. WHAT IS CAPITAL BUDGETING? Capital Budgeting 3 Capital budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm. To evaluate capital budgeting processes, their consistency with the goal of shareholders wealth maximization is of utmost importance.
- 4. THE CAPITAL BUDGETING PROCESS : Generate investment proposal consistent with the firms strategic …objectives. Estimate after tax incremental operating cash flow for the …investment projects. Evaluate project incremental cash flow. Select projects based on a value-maximizing acceptance …criterion. Re evaluate implemented investment projects continually and …perform post audits for completed projects. Capital Budgeting 4
- 6. TRADITIONAL OR NON-DISCOUNTING TECHNIQUES : These techniques don't discount the cash flow to find out there present worth. There two such techniques available i.e., A. The Payback Period B. The Accounting Rate Of Return Capital Budgeting 6
- 7. THE PAYBACK PERIOD: Capital Budgeting 7 The payback period is define as the number of years required for the proposal’s cumulative cash inflow to be equal to its cash outflow. In other words the payback period is the length of the time required to recover the initial cost of the project. Computation of the payback period : The payback period can be calculated into two different situation- a. When Annual Inflows Are Equal: When can inflow generated by the proposal are equal per time period i.e. the cash inflows are in the form of annuity, the payback period can be computed by dividing the cash outflow by the amount of annuity . The Payback Period Is Calculated As Follow: Payback period = Initial Outflow Annual Inflow b. When Annual Inflows Are Unequal: In case the cash inflows from the proposal are not in annuity form then the cumulative cash inflow are used to compute the payback period.
- 8. 8 ACCOUNTING/ AVERAGE RATE OF RETURN: The ARR is based on the accounting concept of return on investment or rate of return. The ARR may be defined as the annualized net income earned on the average funds invested in a project. In other words, the annual return of a project are expressed as a percentage of the net investment in the project. Computation of ARR: Symbolically- Average Annual Profit(After Tax) ARR = * 100 Average investment in the project This clearly shows ARR is a measure based on accounting profits rather than the cash flow and is very similar to the measures of rate of return on capital employed, which is generally used to measures the overall profitability of the firm . The calculation of ARR may be further discussed with reference to equal annual profits and unequal annual profits.
- 9. DISCOUNTED CASH FLOW (DCF) TECHNIQUES : The main DCF techniques for capital budgeting includes: •Net Present Value (NPV) •Internal Rate Of Return (IRR) •Profitability Index (PI) # Each requires estimate of expected cash flow(and their timing)for the project. # Includes cash outflow(cost) and inflow ( revenue or saving) – normally tax effects are also considered Capital Budgeting 9
- 10. DISCOUNTED CASH FLOW (DCF) TECHNIQUES: Capital Budgeting 10 Each requires an estimate of the project’s risk so that an opportunity discount rate (opportunity cost of capital)can be determined. Some times the above data is difficult to obtain – this is the main weakness of all DFC techniques.
- 11. Capital Budgeting 11 NET PRESENT VALUE (NPV) Methods: NPV=PVINFLOW – PVOUTFLOW If NPV > 0, then accept the project ; otherwise reject the project. Strengths Weakness •Resulting number is easy to interpret: shows how wealth will change if the project is accepted. •Acceptance criteria is consistent with shareholder wealth maximization. •Relatively straight forward to calculate •Requires knowledge of finance to use. •An improper NPV analysis may lead to the wrong choices of project when the firm has capital rationing.
- 12. INTERNAL RATE OF RETURN (IRR) IRR is the rate of return that a project generates. Algebraically, IRR can be determined by setting up an NPV equation and solving for a discount rate that makes the NPV=0. Equivalently, IRR is solved by determining the rate that equates the PV of cash inflows to the PV of cash outflows. Methods : Use your financial calculator or a spreadsheet; IRR usually cannot be solved manually. If IRR > opportunity cost of capital (or hurdle rate); then accept the project; otherwise reject it. Capital Budgeting 12
- 13. Capital Budgeting 13 INTERNAL RATE OF RETURN (IRR) STRENGTHS WEAKNESSES •IRR number is easy to interpret: shows the return the project generates. •Acceptance criteria is generally consistent with shareholders wealth maximization. •Requires knowledge of finance to use . •Difficult to calculate – need financial calculator. •It is possible that there exist no IRR or multiple IRR’s for a project and there are several cases when the IRR analysis needs to be adjust in order to make a correct decision.
- 14. Capital Budgeting 14 PROFITABILTY INDEX (PI) PI = PV(cash flow after the initial investments) Initial Investment If PI > 1 , then accept the real investment projects; otherwise reject it.
- 15. Capital Budgeting 15 PROFITABILITY INDEX (PI) STRENGTHS WEAKNESSES •PI number is easy to interpret: shows how many $(in PV terms) you get back per $ invested. •Acceptance criteria is generally consistent with shareholders wealth maximization. •Relatively straightforward to calculate. •Require knowledge of finance to use. •It is possible that PI cannot be used if the initial cash flow is an outflow. •Methods needs to be adjusted when there are mutually exclusive projects.
- 16. Capital Budgeting 16 The DCF techniques ,NPV, IRR & PI, are all good techniques for capital budgeting and allow us to accept or reject investment project consistent with the goal of shareholders wealth maximization. There are times when one techniques output is better for some decision or when a techniques has to be modified given certain circumstances. CAPITAL BUDGETING